A Family of Congruences for Rogers--Ramanujan Subpartitions

Nicolas Smoot

doi:10.1016/j.jnt.2018.09.025

A Family of Congruences for Rogers--Ramanujan Subpartitions

Nicolas Smoot

Research Institute for Symbolic Computation

Research output: Contribution to journal › Article › peer-review

Abstract

In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, A1(m), which counted subpartitions with a structure related to the Rogers–Ramanujan identities. They conjectured the existence of an infinite class of congruences for A1(m), modulo powers of 5. We give an explicit form of this conjecture, and prove it for all powers of 5.

Original language	English
Pages (from-to)	35-60
Number of pages	26
Journal	Journal of Number Theory
Volume	196
DOIs	https://doi.org/10.1016/j.jnt.2018.09.025
Publication status	Published - Mar 2019

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Digital Transformation

Access to Document

10.1016/j.jnt.2018.09.025

Cite this

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abstract = "In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, A1(m), which counted subpartitions with a structure related to the Rogers–Ramanujan identities. They conjectured the existence of an infinite class of congruences for A1(m), modulo powers of 5. We give an explicit form of this conjecture, and prove it for all powers of 5.",

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AB - In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, A1(m), which counted subpartitions with a structure related to the Rogers–Ramanujan identities. They conjectured the existence of an infinite class of congruences for A1(m), modulo powers of 5. We give an explicit form of this conjecture, and prove it for all powers of 5.

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DO - 10.1016/j.jnt.2018.09.025

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JO - Journal of Number Theory

JF - Journal of Number Theory

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